1. Field of the Invention
The present invention relates to an additive sound synthesis process and is more particularly applicable to the creation of musical sounds.
2. Related Art
Additive synthesis normally takes place by a bank of sinusoidal oscillators and processing means making it possible to obtain a sampling of the sinusoids used for obtaining a discretized representation of the musical wave. As a result of the large number of samples necessary for this representation, they are produced by a computer. The calculated samples contained in a memory are converted into a voltage during a digital/analog conversion operation. The sequence of discrete pulses is smoothed by filtering in order to obtain a continuous electric signal, which is amplified and then supplied to a transducer in order to be audible.
It is known that additive sound synthesis identifies the sound phenomenon on superimposing sinusoidal components, whose characteristics can be estimated by a Fourier analysis. The main wave is broken down into a series of frequency components. When the sound is harmonic, the frequency components have multiple frequencies of a so-called fundamental frequency, which corresponds to the pitch and the amplitudes of the components determine the timbre of the sound.
In additive synthesis, the digital signal S(n) representing the synthesized sound is equal to the sum of the j sinusoidal components Cj of frequencies, amplitudes and sometimes phases, which are variable over a period of time: ##EQU1## with EQU Cj(n)=aj(n)Cos [2.pi.fj(n)n/Fe+.alpha.j(n)]
For the component Cj, with a sample n:
fj(n) is the frequency, PA1 aj(n) is the amplitude, PA1 .alpha.j(n) is the phase term, PA1 Fe is the sampling frequency. PA1 choosing a spectral envelope, PA1 then iteratively and for each desired frequency component: PA1 multiplying the spectral envelope by the amplitude of the component weighted by its phase factor, so as to obtain a pattern representing said frequency component, PA1 adding the pattern obtained to the spectrum being constructed,
In known manner, the values of the parameters of the frequencies, amplitudes and phases necessary for the calculation of the signal S(n) during time are supplied to the computer at a so-called refreshing frequency generally below 200 Hz relating to the time constant of the ear.
These parameters can come from an analysis of a sound, an algorithm modelling a certain type of sound (synthesis of an instrument e.g. by the construction of its spectrum) or in pure synthesis data from a musician relating to the frequencies which he wishes to be heard.
As the signal must be generated at a higher sampling frequency than the refreshing frequency of the sets of parameters, there is an interpolation between two successive parameter sets surrounding the instant corresponding to the calculated sample. In practice, the sampling frequency is either 44.1 KHz or 48 KHz, whereas the refreshing frequency is below 200 Hz.
It is necessary to avoid the generation of a succession of sudden variations of values, which would lead to noises or clicks occurring at the refreshing frequency of the parameters.
For each component and starting with the frequency fj(n), an instantaneous phase is calculated: ##EQU2## which makes it possible to calculate the sinusoidal component. The latter is obtained by addressing a table containing the sampled value of Sin x for x assuming M values between 0 and 2 (e.g. M=4096). The value obtained is multiplied by the instantaneous amplitude aj(n) in order to give Cj(n). The values of j components calculated in this way are summated in order to produce the sample S(n).
These stages are repeated for calculating each of the successive samples.
This additive synthesis procedure has a disadvantage of requiring a significant calculation time. Thus, for a given computer, the number of components which can be calculated in real time is low, namely from 8 to 13 on a microprocessor DSP 56000 manufactured by Motorola. Reference can be made in this connection to the article by John Strawn "Implementing Table Look-up Oscillators for Music with the Motorola DSP 5000 Family", Proc. 85th AES Convention, November 88, LA, USA.
The difficulty of producing noise with a random spectral density constitutes another disadvantage of this process. However, the presence of noise is fundamental to the creation of musical sounds. Thus, it makes it possible to credibly simulate wind instruments by the reproduction of breathing and other transients.
Instead of working in a time range as described hereinbefore, another procedure consists of working in the frequency range. Reference should be made in this connection to ICASSP, 1988 entitled "FFT Multi-Frequency Synthesizer", New York, pp. 1431-1434, by Tabei et al.
However, this document only refers to the reconstruction of a signal window. This solution suffers from the disadvantage of adding noise to the signal and also of being incomplete. Thus, it is only possible to reconstruct a signal when the parameters evolve in a complex manner with such a method. This method consisting of synthesizing the signal from a single window is unsuitable for most musical signals (the parameters e.g. evolve when there is a note held with vibrato).